Method for three-dimensionally measuring a 3D aerial image of a lithography mask

ABSTRACT

In a method for three-dimensionally measuring a 3D aerial image in the region around an image plane during the imaging of a lithography mask, which is arranged in an object plane, a selectable imaging scale ratio in mutually perpendicular directions (x, y) is taken into account. For this purpose, an electromagnetic wavefront of imaging light is reconstructed after interaction thereof with the lithography mask. An influencing variable that corresponds to the imaging scale ratio is included. Finally, the 3D aerial image measured with the inclusion of the influencing variable is output. This results in a measuring method with which lithography masks that are optimized for being used with an anamorphic projection optical unit during projection exposure can also be measured.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/410,918, filed on Jan. 20, 2017, which is a continuation ofInternational Application PCT/EP2015/066605, having a filing date ofJul. 21, 2015, which claims priority to German patent application 102014 214 257.1, filed on Jul. 22, 2014, and German patent application 102014 217 229.2, filed on Aug. 28, 2014. The entire contents of the aboveapplications are hereby incorporated by reference in their entirety.

TECHNICAL FIELD

The invention relates to a method for three-dimensionally measuring a 3Daerial image in the region around an image plane during the imaging of alithography mask. The invention also relates to a metrology system forcarrying out this method.

BACKGROUND

Metrology systems of the type mentioned at the beginning are known fromUS 2013/0063716 A1, DE 102 20 815 A1, DE 102 20 816 A1 and US2013/0083321 A1. EP 2 506 061 A1 discloses a projection optical unit fora projection exposure apparatus for producing semiconductor devices thatuses an aperture stop in which the diameter of the stop in two mutuallyperpendicular directions differs by more than 10%. DE 10 2010 040 811 A1describes an anamorphic projection optical unit. US 2008/0036986 A1describes a projection exposure apparatus.

SUMMARY

In a general aspect, the present invention provides a method formeasuring a 3D aerial image of a lithography mask in such a way thatlithography masks that are optimized for being used with an anamorphicprojection optical unit during projection exposure can also be measured.

In another general aspect, the invention is directed to a method forthree-dimensionally measuring a 3D aerial image in the region around animage plane during the imaging of a lithography mask, which is arrangedin an object plane, while taking into account a selectable imaging scaleratio in mutually perpendicular directions (x, y) with the followingsteps: reconstruction of an electromagnetic wavefront of imaging lightafter interaction thereof with the lithography mask, inclusion of aninfluencing variable that corresponds to the imaging scale ratio, andoutput of the 3D aerial image measured with the inclusion of theinfluencing variable.

According to the invention, it has been realized that, for measuringlithography masks that are optimized for use with anamorphiclithographic projection optical units, it is not absolutely necessary touse a metrology system with a likewise anamorphic projection opticalunit. The method according to the invention can also be used with aprojection optical unit that is not anamorphic and, in particular, doesnot have a selectable imaging scale ratio in mutually perpendiculardirections. The anamorphic influence of the lithographic projectionoptical unit is emulated during measurement by including the influencingvariable that is a measure of the imaging scale ratio of thelithographic projection optical unit to be emulated. It is included bymanipulating the reconstructed electromagnetic wavefront, which can beperformed by digital means. Existing metrology systems withnon-anamorphic projection optical units, the image processing softwareof which is correspondingly converted, can in this way also be used inprinciple for the measurement of lithography masks that are optimizedfor use with anamorphic lithographic projection optical units.

Implementations can include one or more of the following features. Thereconstruction of the electromagnetic wavefront can include carrying outthe following steps: measuring a 2D imaging-light intensity distributionin the region of a plane (e.g., 14a) corresponding to the image plane(e.g., 24), displacing the lithography mask (e.g., 5) perpendicularly(z) to the object plane (e.g., 4) by a predetermined displacement (Δz;Δz₁, Δz₂; Δz₁, Δz₂, Δzi), and repeating (e.g., 30) the “measuring” and“displacing” steps until a sufficient number of 2D imaging-lightintensity distributions to reproduce a 3D aerial image are measured. Anincrement of the displacement may be varied as appropriate for therespective measuring task. Measurement results between two actuallymeasured displacement positions may also be obtained by interpolation.An interpolation may take place in the Fourier domain, but also in thespatial domain.

The measurement can be carried out with a measuring optical unit, theimaging scale of which is the same in mutually perpendicular directions(x, y), the inclusion of the influencing variable being performed byconverting the data of the measured 2D imaging-light intensitydistribution. The advantages of measurement with the measuring opticalunit have already been discussed above.

A phase reconstruction can be performed in the reconstruction (e.g., 33)of the electromagnetic wavefront, which can allow a particularly exactreconstruction of the electromagnetic wavefront. A number of differentdigital methods, which are known from the literature, exist for carryingout such a phase reconstruction. The phase reconstruction may beperformed by using a Fourier transformation and an inverse Fouriertransformation.

A defocusing of the imaging of the lithography mask can be varied forthe phase reconstruction, which can be brought about with already knownmetrology systems by displacing the lithography mask perpendicularly tothe object plane, in each case by a predetermined displacement distance.

In the reconstruction (e.g., 33), a manipulation can be performed on theillumination optical unit (e.g., 7), with which the lithography mask(e.g., 5) is illuminated. The manipulation of the illumination opticalunit is a variant that is alternatively or additionally possible and canbe used for the reconstruction of the electromagnetic wavefront. Forthis reconstruction it is possible for the lithography mask to beilluminated from a plurality of different, exactly predeterminedillumination directions and resultant 2D imaging-light intensitydistributions for each of the illumination directions to be measured. Aphase reconstruction may also be carried out with the aid of Fourierptychography. This may involve for example moving a small-aperturepinhole stop through an illumination pupil of the metrology system, inorder to bring about a diversification of the illumination directionsthat is required for Fourier ptychography.

For the reconstruction of the electromagnetic wavefront, an illuminationpupil of the illumination optical unit (e.g., 7) can be varied. Avariation of an illumination pupil of the illumination optical unit ofthe metrology system that is already known in principle from SpatialLight Interference Microscopy (SLIM) may also be used. A phasereconstruction of the electromagnetic wavefront may also be performedinterferometrically, holographically or by using a coherent illuminationof the lithography mask. As an alternative to coherent illumination, therespectively predetermined illumination setting within the illuminationpupil may be used to perform a fine sampling, for which purpose in turna pinhole stop may be used.

The inclusion (e.g., 31) of the influencing variable in the conversionof the data of the wavefront can be performed by a digital simulation ofthe imaging with the imaging scale ratio. The digital simulation of theimaging makes inclusion of the influencing variable that corresponds tothe imaging scale ratio possible without requiring an intervention inthe hardware. The digital simulation may be realized by simulating theeffect of an oval object-side numerical aperture and realizing a roundimage-side numerical aperture during the imaging of the lithographymask. The digital simulation may be performed in the form of a digitalcylindrical lens or in the form of the addition of an astigmaticwavefront.

Apart from a phase reconstruction, an intensity reconstruction may alsobe performed in the reconstruction (e.g., 33) of the electromagneticwavefront. If an intensity reconstruction is performed, an imagingaperture stop with an x/y aspect ratio deviating significantly from 1may be used. The reconstruction calculation in the intensity domain maylikewise be performed with the aid of a Fourier transformation and aninverse transformation. An influencing variable that corresponds to theimaging scale ratio may in this case be included direction-dependentlyin terms of the direction of the Fourier component, in that measurementresults with appropriate selection of a displacement increment are used.For each direction that is assigned a specific imaging scale ratio, ameasurement result with its own displacement increment assigned to thisdirection can then be used.

The intensity reconstruction can be carried out with the followingsteps: measuring (e.g., 28) a 2D imaging-light intensity distribution inthe region of a plane (e.g., 14a) corresponding to the image plane(e.g., 24), displacing the lithography mask (e.g., 5) perpendicularly(z) to the object plane (e.g., 4) by a predetermined displacement (Δz;Δz₁, Δz₂; Δz₁, Δz₂, Δzi), repeating (e.g., 30) the “measuring” and“displacing” steps until a sufficient number of 2D imaging-lightintensity distributions to reproduce a 3D aerial image are measured; andcarrying out an intensity Fourier transformation of the 2D imaging-lightintensity distributions obtained (e.g., FIGS. 11 to 14) to generate acorresponding number of 2D intensity Fourier transforms. The generationof 2D intensity Fourier transforms has been found to be particularlysuitable for intensity reconstruction.

The intensity reconstruction can be carried out with the followingsteps: measuring (e.g., 28) a 2D imaging-light intensity distribution inthe region of a plane (14a) corresponding to the image plane (e.g., 24),displacing the lithography mask (e.g., 5) perpendicularly (z) to theobject plane (e.g., 4) by a predetermined displacement (Δz; Δz₁, Δz₂;Δz₁, Δz₂, Δzi), repeating (e.g., 30) the “measuring” and “displacing”steps until a sufficient number of 2D imaging-light intensitydistributions to reproduce a 3D aerial image are measured, anddistorting the measured 2D imaging-light intensity distributions withthe imaging scale ratio. Distorting the measured 2D imaging lightintensity distributions allows the imaging behavior of a correspondingimaging optical unit to be emulated. After the distortion, an intensityFourier transformation of the 2D imaging-light intensity distributionsobtained may be performed to generate a corresponding number of 2Dintensity Fourier transforms.

Items of information which are included in selected 2D intensity Fouriertransforms that are measured with various displacements of thelithography mask or a test structure can be put together for theintensity reconstruction. The method for three-dimensionally measuring a3D aerial image in the region around an image plane during the imagingof a lithography mask can include selecting the directional componentsof the generated 2D intensity Fourier transforms while taking intoaccount the imaging scale ratio, a displacement (Δzi) during thedisplacing of the lithography mask (e.g., 5) perpendicularly to theobject plane (e.g., 4) scaling with the alignment (φ) of the directionalcomponents, to generate in each case a partial synthetic 2D intensityFourier transform; adding the generated partial synthetic 2D intensityFourier transforms to form an overall synthetic 2D intensity Fouriertransform; and carrying out an inverse intensity Fourier transformationof the overall synthetic 2D intensity Fourier transforms to produce asynthetic raw image. A set of 2D imaging-light intensity distributionsthat were measured for predetermined displacements of the lithographymask is used for this, and a directional component of the intensityFourier transforms is respectively selected from this set with the aidof an assignment function. These various directional components are thenput together. The assignment function is selected so as to ensure atransition that is as smooth as possible between those directionalcomponents that correspond to extreme values of the imaging scales. Theassignment function is in particular monotonic and may be continuouslydifferentiable, in particular multiply continuously differentiable.

A result image (e.g., FIG. 25) can be produced by distorting thesynthetic raw image (e.g., FIG. 24) with the imaging scale ratio. Theadditional distortion step makes it possible in turn to emulate animaging optical unit with a corresponding imaging scale ratio. As analternative to a distortion of the synthetic raw image, a distortion mayalso be performed before carrying out an intensity Fouriertransformation of measured 2D imaging-light intensity distributions. Inthis case, the measured 2D imaging-light intensity distributions arefirst distorted before the steps of intensity Fourier transformation,generation of an overall synthetic 2D intensity Fourier transform andintensity inverse Fourier transformation are performed.

The distortion may be performed digitally, therefore by conversion ofthe measured values.

The selection of the directional components of the generated 2Dintensity Fourier transforms (e.g., FIGS. 15 to 18) can be performed bymultiplying each of the generated 2D intensity Fourier transforms (e.g.,FIGS. 15 to 18) by an assigned selection function (e.g., FIGS. 19 to 22)for the selection of predetermined angle sectors of the 2D intensityFourier transforms (e.g., FIGS. 15 to 18), the selection function beingdependent on the displacement (Δzi) perpendicularly to the object plane(e.g., 4) and on the imaging scale ratio, to generate the respectivepartial synthetic 2D Fourier transforms. The selection of thedirectional components of the generated 2D intensity Fourier transformscan be realized numerically with comparatively simple means. Theselection function may be chosen so as to make allowance for anormalizing condition, which ensures that each direction is selectedwith equal entitlement.

The method for three-dimensionally measuring a 3D aerial image in theregion around an image plane during the imaging of a lithography maskcan include the use of a digital selection function, which can benumerically implemented in a particularly easy way. As an alternative toa digital selection function, which can only assume the values 0 and 1,a selection function with a continuous transition between the values 0and 1 may be used.

In another general aspect of the invention, a metrology system (e.g., 2)for carrying out the method for three-dimensionally measuring a 3Daerial image in the region around an image plane during the imaging of alithography mask can include an illumination optical unit (e.g., 7) forilluminating the lithography mask to be examined and an imaging opticalunit (e.g., 13) for imaging the object towards a spatially resolvingdetection device (e.g., 14). The advantages of the metrology systemcorrespond to those that have already been explained above withreference to the method according to the invention.

BRIEF DESCRIPTION OF DRAWINGS

An exemplary embodiment of the invention is explained in greater detailbelow with reference to the drawing. In said drawing:

FIG. 1 shows highly schematically in a plan view looking in a directionperpendicular to a plane of incidence a metrology system for theexamination of an object in the form of a lithography mask with EUVillumination and imaging light by use of an illumination optical unitand an imaging optical unit, each of which is represented extremelyschematically;

FIG. 2 shows an illumination setting, that is to say an intensitydistribution of illumination light in a pupil plane of the illuminationoptical unit, for an illumination of the object;

FIG. 3 shows a plan view of the object to be imaged;

FIG. 4 shows a plan view of an imaging aperture stop for the marginaldelimitation of an imaging light beam in the imaging optical unit;

FIG. 5 shows less schematically than in FIG. 1 a side view of anarrangement of a lithographic projection optical unit between the objectto be imaged and a wafer, the object being the one that was examined inadvance with the metrology system shown in FIG. 1;

FIG. 6 shows schematically in a section in a plane of incidence areflection of the illumination and imaging light at the object duringthe projection exposure;

FIG. 7 shows a section through the incident illumination light beam andthe emerging imaging light beam according to line VII-VII in FIG. 6;

FIG. 8 shows a flow diagram of a method for three-dimensionallymeasuring a 3D aerial image in the region around an image plane duringthe imaging of the lithography mask;

FIG. 9 shows a flow diagram that illustrates in greater detail methodsteps for the inclusion of an influencing variable that corresponds tothe ratio of imaging scales of the projection optical unit in mutuallyperpendicular directions;

FIG. 10 shows in a diagram a dependence of a displacement Δzi of a fieldplane from an optimum focal plane of the imaging optical unit, thisdisplacement Δzi being used for an intensity reconstruction during themeasurement of a 3D aerial image, on an angle φ of a directionalcomponent of a Fourier transform used for the calculation of the 3Daerial image, the dependence being shown for a given imaging scale ratioof the imaging optical unit and for various reconstruction displacementsof the object plane from the optimum focal plane of the imaging opticalunit and also for two different continuously differentiable functionsdescribing the angle dependence;

FIGS. 11 to 14 show in each case a 2D intensity distribution of animaging of a rectangular test structure for various defocusingdisplacements Δz of the test structure, respectively recorded in the xyplane;

FIGS. 15 to 18 show the absolute value of the 2D intensity Fouriertransforms assigned to the intensity distributions of FIGS. 11 to 14;

FIGS. 19 to 22 show the digital selection functions assigned to theFourier transforms shown in FIGS. 15 to 18 for the selection of specificdirectional components of the Fourier transforms;

FIG. 23 shows the absolute value of an overall synthetic 2D Fouriertransform generated with the aid of the intensity Fourier transformsshown in FIGS. 15 to 18 and the selection functions shown in FIGS. 19 to22;

FIG. 24 shows a synthetic image as the result of an inverse Fouriertransformation of the overall Fourier transform shown in FIG. 23;

FIG. 25 shows a synthetic result image after distortion of the syntheticimage shown in FIG. 24 with a predetermined imaging scale ratio of animaging optical unit to be emulated or to be reconstructed.

DETAILED DESCRIPTION

A Cartesian xyz-coordinate system is used below to facilitate theillustration of positional relationships. In FIG. 1, the x axis runsperpendicularly to the plane of the drawing into the latter. In FIG. 1,the y axis runs upwards. In FIG. 1, the z axis runs towards the right.

FIG. 1 shows in a view corresponding to a meridional section a beam pathof EUV illumination light and imaging light 1 in a metrology system 2for the examination of an object 5, arranged in object field 3 in anobject plane 4, in the form of a reticle or a lithography mask with theEUV illumination light 1. The metrology system 2 is used for analyzing athree-dimensional (3D) aerial image (Aerial Image Metrology System) andserves for simulating and analyzing the effects of properties oflithography masks, known as reticles, which in turn are used duringprojection exposure for producing semiconductor devices, on the opticalimaging by projection optical units within a projection exposureapparatus. Such systems are known from US 2013/0063716 A1 (cf. FIG. 3therein), from DE 102 20 815 A1 (cf. FIG. 9 therein) and from DE 102 20816 A1 (cf. FIG. 2 therein) and from US 2013/0083321 A1.

The illumination light 1 is reflected at the object 5. The plane ofincidence of the illumination light 1 lies parallel to the yz plane.

The EUV illumination light 1 is produced by an EUV light source 6. Thelight source 6 may be a laser plasma source (LPP; laser produced plasma)or a discharge source (DPP; discharge produced plasma). In principle, asynchrotron-based light source may also be used, for example a freeelectron laser (FEL). A used wavelength of the EUV light source may liein the range between 5 nm and 30 nm. In principle, in the case of avariant of the metrology system 2, a light source for another usedwavelength may also be used instead of the light source 6, for example alight source for a used wavelength of 193 nm.

Depending on the configuration of the metrology system 2, it may be usedfor a reflecting object 5 or for a transmitting object 5. An example ofa transmitting object is a phase mask.

An illumination optical unit 7 of the metrology system 2 is arrangedbetween the light source 6 and the object 5. The illumination opticalunit 7 serves for the illumination of the object 5 to be examined with adefined illumination intensity distribution over the object field 3 andat the same time with a defined illumination angle distribution, withwhich the field points of the object field 3 are illuminated.

FIG. 2 shows a corresponding illumination setting, which can be set forthe illumination optical unit 7. Represented in FIG. 2 is an intensitydistribution of the illumination light 1 in a pupil plane 8 (cf. FIG. 1)or in a plane of the illumination optical unit 7 conjugate thereto. Theillumination setting takes the form for example of a hexapole settingwith six illumination poles 9.

The six illumination poles 9 lie within an elliptical outer edge contour10, which is indicated in a dashed manner in FIG. 2. This edge contour10 follows an ellipse with a ratio between the major semiaxis parallelto the x axis and the minor semiaxis parallel to the y axis of 2:1.Other axis ratios of the elliptical edge contour 10 in the range from10:1 to 1.1:1 are also possible, for example of 1.5:1, 1.6:1, 2.5:1,3:1, 4:1, 5:1 or 8:1.

The elliptical edge contour 10 is produced by an illumination aperturestop 11 of the illumination optical unit 7, which marginally delimits abeam of the illumination light 1 that is incident on the illuminationaperture stop 11. Correspondingly, in a stop plane extending parallel tothe xy plane, the illumination aperture stop 11 has in the two mutuallyperpendicular directions x and y two stop diameters that differ from oneanother by at least 10%, in the present case by 100%, the correspondingequivalents of which are denoted in FIG. 2 by Bx and By. Theillumination aperture stop 11 has the greater stop diameter Bxperpendicular to the plane of incidence yz of the illumination light 1on the object 5.

The metrology system 2 is designed for the examination of anamorphicmasks with different structure scaling factors in x and y. Such masksare suitable for producing semiconductor elements by use of anamorphicprojection apparatuses.

A numerical aperture of the illumination and imaging light 1 in the xzplane may be 0.125 on the reticle side and in the yz plane 0.0625 on thereticle side.

FIG. 3 shows a plan view of the object 5. Structures on the reticle 5are stretched in the y direction by a factor of 2. This means that apartial structure, for example the rectangular structure 12 in the lowerright-hand corner of the object 5 shown in FIG. 3, which is intended tobe imaged in a 1:1 structure, has an x/y aspect ratio of 1:2.

After reflection at the object 5, the illumination and imaging light 1enters an imaging optical unit or projection optical unit 13 of themetrology system 2, which in FIG. 1 is likewise schematically indicatedby a dashed border. The imaging optical unit 13 serves for imaging theobject 5 towards a spatially resolving detection device 14 of themetrology system 2. The detection device 14 is designed for example as aCCD detector.

The imaging optical unit 13 comprises an imaging aperture stop 15arranged downstream of the object 5 in the beam path (cf. also FIG. 4)for the marginal delimitation of an imaging light beam. The imagingaperture stop 15 is arranged in a pupil plane 8 a of the imaging opticalunit 13. The pupil planes 8 and 8 a may coincide; this is not mandatoryhowever.

It is also possible to dispense with the imaging aperture stop 15 in themetrology system 2.

The imaging aperture stop 15 has an elliptical edge contour 16 with anx/y semiaxis ratio of 2:1. Therefore, in a stop plane extending parallelto the xy plane, the imaging aperture stop 15 has in two mutuallyperpendicular directions x, y two stop diameters that differ from oneanother by at least 10%, which are in turn denoted in FIG. 4 by Bx andBy. What was said above with respect to the corresponding diameter ratioof the illumination aperture stop 11 applies to the diameter ratio Bx:Byin the range between 10:1 and 1.1:1.

The imaging aperture stop 15 also has the greater stop diameter Bxperpendicular to the plane of incidence yz of the illumination andimaging light 1 on the object 5. Also in the case of the imagingaperture stop 15, the diameter Bx is twice the diameter By.

The detection device 14 is in signaling connection with a digital imageprocessing device 17.

The object 5 is carried by an object holder 18. This object holder canbe displaced by a displacement drive 19 on the one hand parallel to thexy plane and on the other hand perpendicularly to this plane, that is tosay in the z direction. The displacement drive 19, as also the entireoperation of the metrology system 2, is controlled by a central controldevice 20, which, in a way that is not represented any morespecifically, is in signaling connection with the components to becontrolled.

The optical set-up of the metrology system 2 serves for the most exactpossible emulation of an illumination and an imaging in the course of aprojection exposure of the object 5 during the projection-lithographicproduction of semiconductor devices.

FIG. 5 shows the imaging ratios of a lithographic projection opticalunit 21 that is used during such a lithographic projection exposure. Asa difference from FIG. 1, FIG. 5 shows a transmitting illumination ofthe object 5 instead of the actually occurring reflecting illumination.A structuring of this illumination light beam 22 on the basis of adefined illumination setting with discrete illumination poles isindicated in an illumination light beam 22 of the illumination andimaging light 1.

The projection optical unit 21, which is part of a projection exposureapparatus that is not otherwise represented, is of an anamorphicconfiguration, and therefore has a different imaging scale in the xzplane than in the yz plane. An object-side numerical aperture of theprojection optical unit 21 is 0.125 in the xz plane and 0.0625 in the yzplane. An image-side numerical aperture of the projection optical unit21 is 0.5 both for the xz plane and for the yz plane. This gives animaging scale of 4× in the xz plane and an imaging scale of 8× in the yzplane, that is to say a reduction factor on the one hand of 4 and on theother hand of 8.

During the projection exposure, the projection optical unit 21 projectsan image of the object field 3 into an image field 23 in an image plane24, in which a wafer 25 is arranged.

As a difference from the projection optical unit 21 of the projectionexposure apparatus, the projection optical unit 13 of the metrologysystem 1 is not anamorphic, but instead has the same magnifying imagingscale β_(MS) of more than 100, for example of 500 or of 850, both in thexz plane and in the yz plane. The projection optical unit 13 of themetrology system is therefore isomorphic.

FIGS. 6 and 7 illustrate the reflection ratios when using anillumination with an elliptical edge contour, which can then be used inthe reflection of an anamorphic projection optical unit adaptedcorrespondingly thereto, such as the projection optical unit 21, or anoptical unit with an elliptical imaging aperture stop, as in the case ofthe projection optical unit 13. On account of the elliptical crosssection on the one hand of the illumination light beam 22 and on theother hand of an imaging light beam 26 reflected by the object 5, asmall chief-ray angle of incidence CRA of 6° or less can be realized,since the light beams 22, 26 respectively have the same numericalaperture in the yz plane of 0.0625. In the xz plane perpendicularthereto, the light beams 22 and 26 have the greater numerical apertureof 0.125, which does not cause any disturbance there.

A central axis, from which the chief-ray angle CRA is measured and whichis perpendicular to the object plane 4, is denoted in FIGS. 6 and 7 byA.

Data that can be used to deduce an imaging behavior of the structure ofthe object 5 that is illuminated in the object field 3 by the projectionoptical unit 21 in the region of the image plane 24 are generated duringthe 3D aerial-image measurement. For this purpose, the metrology system2 is used, the imaging scale ratio of 2:1 of the projection optical unit21 in the two mutually perpendicular directions y and x, that is to sayin the two mutually perpendicular planes yz and xz, being taken intoaccount by using a metrology system projection optical unit 13 that isnot anamorphic.

The method for 3D aerial image measurement is explained below on thebasis of FIGS. 8 and 9.

First, the object 5 to be measured, that is to say the lithography maskto be measured, is provided in a step 27. Then, the intensitydistribution of the imaging light 1 is measured in the region of animage plane 14 a, in which the detection device 14 of the metrologysystem 1 is arranged. This takes place in a measuring step 28. In themeasuring step 28, the detection device 14 detects a 2D imaging-lightintensity distribution within a detection field, into which an image ofthe object field 3 is projected by the projection optical unit 13 of themetrology system. The measured intensity distribution is then in eachcase stored and passed on to the digital image processing device 17.

Then the lithography mask 5 is displaced with the aid of thedisplacement drive 19 perpendicularly to the object plane 4 by apredetermined displacement Δz. This takes place in a displacement step29.

The measuring step 28 and the displacement step 29 are then repeated bycarrying out a repetition step 30 as often as is needed until asufficient number of 2D imaging-light intensity distributions toreproduce a 3D aerial image are measured by use of the detection device14. By repeating the measuring step 28 and the displacement step 29 fordifferent z positions of the object 5, the 2D imaging-light intensitydistribution is therefore measured for example at five, seven, nine oreleven positions, each lying Δz apart, the object 5 lying exactly in theobject plane 4 in the case of a midway displacement step 29. In FIG. 1,corresponding displacement z positions of the object 5 are indicated ina dash-dotted manner. The case in which five z positions, each lying Δzapart, are measured is shown, the z position that is shown in FIG. 1, inwhich the object 5 lies in the object plane 4, representing the middleof the five z positions to be measured.

In the case of this measuring method, the third dimension of the 3Daerial image, to be specific the z dimension, is made accessible to themeasurement by z displacement of the object 5. Since the 3D aerial imageis intended to emulate an anamorphic imaging, to be specific an imagingby the lithographic projection optical unit 21, in the region of theimage plane 14 a each displacement step 29 leads to a defocusing in thez direction. Defocusing values on the one hand in the xz plane and onthe other hand in the yz plane differ from one another on account of thexz/yz imaging scale ratio of the lithographic projection optical unit 21to be emulated. The difference between the imaging scale ratios on theone hand of the isomorphic projection optical unit 13 of the metrologysystem and on the other hand of the anamorphic projection optical unit21 of the projection exposure apparatus to be emulated is taken intoaccount in the measuring method by including an influencing variablethat corresponds to the ratio of the imaging scales of the lithographicprojection optical unit 21. This takes place in an inclusion step 31,which is represented in greater detail in the flow diagram of FIG. 9.

The measurement is carried out with a measuring optical unit of themetrology system 1, the imaging scale of which is the same in mutuallyperpendicular directions (xz/yz). The inclusion step 31 is performedexclusively by converting the data of the measured 2D imaging-lightintensity distribution. This conversion is carried out by the digitalimage processing device 17.

When carrying out the inclusion step 31, first the data records of themeasuring steps 28 are referred to, that is to say the various measured2D imaging-light intensity distributions at the various z positions ofthe object 5 that were measured in the course of the previous sequenceof the repeating steps “measuring step 28/displacement step 29” andstored in a memory of the digital image processing device 17. This takesplace in a reference step 32.

In preparation for the inclusion, an electromagnetic wavefront of theimaging light 1 after interaction of the imaging light 1 with the object5 is reconstructed in a reconstruction step 33 from the data used forreference in this way. This reconstruction takes place in particular inthe region of the image plane 14 a of the metrology system 1. In thereconstruction step 33, a phase reconstruction of the electromagneticwavefront of the imaging light 1 may be performed. In particular, thephase and amplitude of a 3D object spectrum and the partially coherentsuperimposition thereof are reconstructed. A polarization-dependentreconstruction does not take place.

Various methods of phase reconstruction that are already known from theliterature may be used for carrying out the reconstruction step 33.These include methods that include various 2D imaging-light intensitydistribution sequences produced by correspondingly carrying out theseries of steps 28 to 30 repeatedly, part of the optical system of themetrology system 1 being changed in each of these sequences, which isalso known as diversification. Steps 28 to 30 may therefore representpart of the phase reconstruction and be used in the reconstruction ofthe wavefront in step 33.

In the case of a variant of the phase reconstruction, a defocusingdiversification takes place. This has already been discussed above byexplaining steps 28 to 30.

Algorithms that are used here may be for example: Transport of IntensityEquation, Iterative Fourier Transform Algorithms (IFTA, e.g.Gerchberg-Saxton) or methods of optimization, for example by use ofbackpropagation. The Transport of Intensity Equation (TIE) algorithm isdescribed in the technical article “Critical assessment of the transportof intensity equation as a phase recovery technique in opticallithography”, Aamod Shanker; Martin Sczyrba; Brid Connolly; FranklinKalk; Andy Neureuther; and Laura Waller, Proc. SPIE 9052, OpticalMicrolithography XXVII, 90521D (Mar. 31, 2014); DOI:10.1117/12.2048278.The “Gerchberg-Saxton” algorithm is described in Fienup, J. R. (Aug. 1,1982) “Phase retrieval algorithms: a comparison”, Applied Optics 21(15): 2758-2769. Bibcode:1982 Applied Optics, Vol. 21, pp. 2758-2769,DOI:10.1364/AO.21.002758. The “backpropagation” method of optimizationis described in “General framework for quantitative three-dimensionalreconstruction from arbitrary detection geometries in TEM”, Phys. Rev. B87, 184108—published May 13, 2013, Wouter Van den Broek and Christoph T.Koch.

A further variant for an algorithm that can be used in the phasereconstruction is Stokes polarimetry. This algorithm is described forexample in Optics Express, Jun. 2, 2014; 22(11):14031-40; DOI:10.1364/OE.22.014031, “All-digital wavefront sensing for structuredlight beams”, Dudley A, Milione G, Alfano R R, and Forbes A.

When using a phase reconstruction, it is also possible to dispense withthe elliptical imaging aperture stop 15. The optical effect of theaperture stop can also be brought about digitally.

As an alternative to a defocusing diversification, an illuminationdirection diversification can also be carried out for carrying out thereconstruction step 33. An example of this is Fourier ptychography. Thisalgorithm is described in the technical article “Wide-field,high-resolution Fourier ptychographic microscopy”, Guoan Zheng et al.,Nature Photonics, Advance online publication 28 Jul. 2013,DOI:10.1038/NPHOTON.2013.187.

This involves measuring a 2D imaging-light intensity distribution foreach illumination direction and calculating back to the phase andamplitude of the electromagnetic wavefront by use of an algorithm. Thealgorithms IFTA or backpropagation can in turn be used here.

A further possibility for carrying out the reconstruction step 33 is ageneral pupil manipulation, as is used for example in “Spatial LightInterference Microscopy (SLIM, cf. the technical article Wang et al.Optics Express, 2011, volume 19, no. 2, page 1017). Here, four imagesare recorded for example, each with a different phase-shifting mask,which is arranged in a detection pupil, that is to say for example inthe pupil plane 8 a of the projection optical unit 13 of the metrologysystem 1.

In principle, the phase reconstruction of the electromagnetic wavefrontmay also be performed without such a diversification. Examples of thisare methods of interferometry and digital holography. In interferometry,a reference beam is needed. In digital holography, for example, agrating is introduced into the detection pupil. The individual orders ofdiffraction are then brought to a state of interference on the detector.By way of example, these methods of interferometry and digitalholography are described in U. Schnars, W. Jüptner (2005), DigitalHolography, Springer, and Wen, Han; Andrew G. Gomella, Ajay Patel,Susanna K. Lynch, Nicole Y. Morgan, Stasia A. Anderson, Eric E. Bennett,Xianghui Xiao, Chian Liu, Douglas E. Wolfe (2013), “Subnanoradian X-rayphase-contrast imaging using a far-field interferometer of nanometricphase gratings”, Nature Communications 4, Bibcode:2013NatCo . . .4E2659W, DOI:10.1038/ncomms3659.

For a given illumination setting, for which the imaging function of thelithographic projection optical unit 21 is intended to be emulated bythe metrology system 1, a phase reconstruction can be realized by finesampling of the illumination pupil used with these illuminationsettings, for example of the intensity distribution shown in FIG. 2. Theillumination setting used is in this case approximated by many smallvirtually coherent illumination monopoles, which are measuredsequentially. Such monopoles are indicated in FIG. 2 by way of exampleat 34. A phase reconstruction is then carried out for each of thesemonopoles 34, so that, after interaction with the object 5, thepartially coherent wave to be determined can be described as asuperimposition of approximately coherent waves, that is to say theresults of the respective phase reconstruction for monopoleillumination. Such scanning of the illumination pupil is used in Fourierptychography as diversification. A partially coherent field cantherefore be described as a superimposition of many virtually coherentfields that are produced by the monopole sampling.

After the reconstruction step 33, a digital simulation of the imaging isperformed with the imaging scale ratio of the lithographic projectionoptical unit 25. This is performed in a digital simulation step 35.

The electromagnetic wavefront calculated in the reconstruction step 33is thereby manipulated in the same way as it would be manipulated in thepropagation by a corresponding anamorphic system. This may take place byusing a digital elliptical imaging aperture stop corresponding to theimaging aperture stop 15 explained above. At the same time, it must beensured by the digital manipulation that, on the image side, as also inthe case of the lithographic projection optical unit 25, the numericalaperture in the xz plane is equal to the numerical aperture in the yzplane. Such a digital manipulation may be performed by a digitalcylindrical lens or by adding an astigmatic wavefront. The addition ofan astigmatic wavefront may be performed by addition of a contributionof a Zernike polynomial Z5. Zernike polynomials Zi (i=1, 2, . . . ) areknown for example in the Fringe notation from the mathematical andoptical literature. An example of this notation is provided by the CodeV Manual, version 10.4, pages C-6 ff.

The resultant astigmatic wavefront can then be calculated in eachpropagation plane.

Correspondingly, the output of the resultant 3D aerial image with theinclusion of the influencing variable can then be output in an outputstep 36.

The phase reconstruction may include a Fourier transformation step, withwhich a complex, that is to say phase-including, amplitude distributionis calculated from a calculated phase. After digital astigmatismmanipulation, it is then possible to calculate back into the image fieldwith the aid of an inverse Fourier transformation.

In the course of the phase reconstruction, a three-dimensional (3D)Fourier transformation may also take place.

Alternatively, an intensity Fourier transformation of the 2Dimaging-light intensity distributions determined in the sequence ofsteps 28 to 30 may be carried out to carry out the reconstruction step33, for which purpose these intensity distributions are provided inadvance with periodic boundary conditions by use of known mathematicaltechniques. In this connection, reference is made to WO 2008/025433 A2and DE 10 2007 009 661 A1.

The inclusion step 31 is then performed by selecting the xy directionalcomponents of the generated intensity Fourier transformations whiletaking into account the xy imaging scale ratio of the lithographicprojection optical unit 21. A Fourier image is therefore composed, the xcomponent of which was recorded during a displacement by a firstincrement Δz₁ with a sequence of method steps 28 to 30, and the ycomponent of which is provided by using Fourier components of theintensity distributions of a sequence that were recorded with anincremental ratio Δz₂. For directional components that form an angle φwith the x axis of between 0° and 90°, Fourier-transformed 2D intensitydata that were recorded with an intermediate increment Δzi are used. Therespective increment Δzi scales with the angle φ of the directionconsidered in each case of the Fourier component and the x axis.

The function Δzi (φ) can be varied between the increments Δz₁ for the xaxis and the increments Δz₂ for the y axis linearly or by use of anappropriately selected matching function, for example by use of aquadratic function, a sine function and a sine² function.

The Δzi incremental measurements of the 2D imaging-light intensitydistributions do not all have to be carried out in reality; if ameasurement for a z value between two measurements carried out inreality is needed, an interpolation between these two 2D imaging-lightintensity distributions can also be carried out. This interpolation maybe performed for example with the aid of a nearest-neighborhood, linear,bicubic or spline interpolation function. The interpolation may takeplace in the Fourier domain, but also in the spatial domain.

An imaging with the metrology system 2 may be carried out with anelliptical imaging aperture stop 15, but alternatively also with an ovalor rectangular stop. If no phase reconstruction is carried out, it isnecessary to use an imaging aperture stop with an x/y aspect ratio thatcorresponds to the ratio of the imaging scale in the x and y directionsof an imaging optical unit to be emulated or to be reconstructed, thatis to say has for example an aspect or diameter ratio in the rangebetween 10:1 and 1.1:1.

The Fourier image thus manipulated and composed of the variousdirectional components is then transformed back by use of an inverseFourier transformation, so that the desired 3D aerial image is obtained.

The resultant image intensity distribution may then also be distorted bysoftware, in particular be scaled differently in the x direction than inthe y direction, in order to reproduce an amorphism produced by thelithographic projection optical unit 21.

Steps 28 to 30 are therefore not mandatory. After the providing step 27,a reconstruction of the wavefront may also be performed in thereconstruction step 33 by one of the variants described above.

A method for three-dimensionally measuring a 3D aerial image in theregion around the image plane 24 during the imaging of the lithographymask 5, which is arranged in the object plane 4, while taking intoaccount a selectable imaging scale ratio of an imaging optical unit tobe emulated or to be reconstructed by using intensity reconstruction ofan electromagnetic wavefront of the imaging light 1, is explained instill more detail below on the basis of FIG. 10 ff.

This involves first measuring a stack of 2D imaging-light intensitydistributions respectively differing by a Δz displacement of the teststructure in the region of the plane 14 a with the detection device 14by repeating steps 28 to 30. This takes place with the imaging aperturestop 15 used, shown in FIG. 4.

FIGS. 11 to 14 show by way of example for a rectangle 5 as an example ofa test structure, which is used instead of the lithography mask 5,various measurement results for the resultant 2D imaging-light intensitydistribution. The rectangle has an x/y aspect ratio of 1:2.

FIG. 11 shows the measured 2D imaging-light intensity distribution for aresultant image-side defocusing Δz of 1600 nm.

FIG. 12 shows the measured 2D imaging-light intensity distribution for adefocusing Δz of 2500 nm.

FIG. 13 shows the measured 2D imaging-light intensity distribution for adefocusing Δz of 4900 nm.

FIG. 14 shows the measured 2D imaging-light intensity distribution for adefocusing Δz of 6400 nm.

The progressive defocusing that can be seen in FIGS. 11 to 14 appears tobe weaker in the y direction for a given displacement Δz than in the xdirection, which is explained by the Bx/By aspect ratio of the imagingaperture stop 15, which leads to a greater depth of field in the ydirection in comparison with the x direction.

To achieve an intensity reconstruction of the 3D aerial image of theimaging optical unit to be emulated with a predetermined imaging scaleratio different from 1, a conversion of the measured focus stack with amultiplicity of 2D imaging-light intensity distributions of the typeshown in FIGS. 11 to 14 for various displacements Δz into a syntheticresult image of the 3D aerial image of this imaging optical unit thentakes place.

By way of example, a magnification scale of the imaging optical unit 21to be emulated of ¼ in the x direction, β_(x), and of ⅛ in the ydirection, β_(y), is assumed. The imaging optical unit 13 of themetrology system 2 has an isomorphic magnification factor β_(MS) of 850.

The displacement Δz of the test structure or the lithography mask 5 isalso referred to below as Δz_(LM).

With the aid of selected 2D imaging-light intensity distributions forspecific displacements Δz, as shown by way of example in FIGS. 11 and14, a synthetic image of the lithographic projection optical unit 21 isthen produced. For this purpose, an intensity Fourier transformation ofeach of the 2D imaging-light intensity distributions is generated. Theresult is in each case a 2D intensity Fourier transform. By way ofexample, the absolute value of the 2D intensity Fourier transform of the2D imaging-light intensity distributions shown in FIGS. 11 to 14 isshown in FIGS. 15 to 18.

A new synthetic result image is then produced from these intensityFourier transforms. For this purpose, directional components of thefirst-generated 2D intensity Fourier transforms are selected, takinginto account the imaging scale ratio of the lithographic projectionoptical unit 21. A displacement Δzi of a 2D imaging-light intensitydistribution respectively selected for this purpose scales here with thealignment of the directional components. The following procedure isfollowed for this: The intensities and phases (that is to say real andimaginary components) of the Fourier image that was recorded in theplane Δzi=Δz_(LM)/β_(x) ² are used on the x axis.

The intensities and phases of the Fourier image that was recorded in theplane Δzi=Δz_(LM)/β_(y) ² are used on the y axis.

The intensities and phases of a Fourier image that was recorded in adefocusing plane Δzi between Δz_(LM)/β_(x) ² and Δz_(LM)/β_(y) ² areused for all of the pixels in between. The function for theinterpolating calculation of the defocusing is intended to be continuousand advantageously continuously differentiable and advantageouslymonotonic from 0° to 90°.

Two examples of an assignment of respective Δz displacement positions tothe directional components, that is to say the various angles φ, aregiven below:Δzi=Δz _(LM)*1/(β_(x)+(β_(y)−β_(x))*sin²φ)²   (=example assignmentfunction 1)Δzi=Δz _(LM)*(1/β_(x)+(1/β_(y)−1/β_(x))*sin²φ)²   (=example assignmentfunction 2)

FIG. 10 illustrates the profile of these example assignment functions,that is to say the dependence Δzi (φ) for values of Δz_(LM) of −100 nm,−50 nm, 0 nm, 50 nm and 100 nm. The curves assigned to the exampleassignment function 1 are denoted by BF1 and the curves assigned to theexample assignment function 2 are denoted by BF2.

A further example of an assignment function in the manner of the exampleassignment functions 1 and 2 described above is the mean value of thesetwo example assignment functions.

A focus stack with very many images and a very small increment is neededfor this calculation. In practice, however, usually fewer images aremeasured (for example to save measuring time) and a greater increment ischosen. In this case, the images between the various measured images canbe interpolated. The interpolation may be performed in the image domain(that is to say before the Fourier transformation) or in the Fourierdomain (after the Fourier transformation). Depending on what accuracy isrequired, nearest neighbour, linear, bicubic, spline or some othermethod comes into consideration as the method of interpolation.

Advantageously, the overall focal region is chosen to be of such a sizethat it is only necessary to interpolate and not extrapolate between thefocal planes.

A numerical realization of a directional component selectioncorresponding to one of these example assignment functions isillustrated by digital selection functions shown in FIGS. 19 to 22.There, the digital selection functions have the value 1 where there arewhite areas, and the value 0 everywhere else.

On the basis of the four 2D imaging-light intensity distributionsmeasured according to FIGS. 11 to 14, an overly coarse determination ofthe result image is shown, with correspondingly just four differentdefocusing values and assigned selection functions. The latter arechosen such that each point on the x/y area defined by the digitalselection functions is selected precisely once. The assignment of thesedirectional components φ to the defocusing value Δzi is performed hereby way of the assignment example function BF1, that is to say theuppermost curve in FIG. 10.

A result image for Δz_(LM)=100 nm is calculated. The intensity Fouriertransform shown in FIG. 15 is selected for the x axis of this resultimage. For this purpose, this intensity Fourier transform shown in FIG.15 is multiplied by the digital selection function shown in FIG. 19,which is 1 for values that lie in the region of the x axis (φ≈0) and 0for all other values.

The selection function shown in FIG. 20 is assigned to the intensityFourier transform shown in FIG. 16 and covers the value φ approximatelyequal to 30°.

FIG. 21 shows the digital selection function for the intensity Fouriertransform shown in FIG. 17 (directional component φ approximately equalto 60°).

FIG. 22 shows the digital selection function for the intensity Fouriertransform shown in FIG. 18 (φ approximately equal to 90°).

Therefore, a selection of predetermined angle sectors of the 2Dintensity Fourier transforms shown in FIGS. 15 to 18 takes place by wayof the selection functions 19 to 22.

Numerically, the intensity Fourier transform shown in FIG. 15 istherefore multiplied by the digital selection function shown in FIG. 19;the intensity Fourier transform shown in FIG. 16 is multiplied by thedigital selection function shown in FIG. 20, the intensity Fouriertransform shown in FIG. 17 is multiplied by the digital selectionfunction shown in FIG. 21 and the intensity Fourier transform shown inFIG. 18 is multiplied by the digital selection function shown in FIG.22. The results of these multiplications are added and give an overallsynthetic 2D intensity Fourier transform. The absolute value thereof isrepresented in FIG. 23. Therefore, partial synthetic 2D intensityFourier transforms generated in an intermediate step and representing ineach case the result of the individual multiplications are added to oneanother. An inverse Fourier transformation of this overall synthetic 2Dintensity Fourier transform gives a synthetic raw image shown in FIG.24.

This synthetic raw image shown in FIG. 24 is then distorted with theimaging scale ratio of the lithographic projection optical unit 21, sothat the result image shown in FIG. 25 is obtained as the result imagefor the defocusing Δz_(LM) to be emulated of 100 nm. As expected, withthis defocusing the edges of the imaged test structure are washed outequally in the x and y directions, since there is a balancing out of thedifference in the depth of field in the x and y directions on account ofthe imaging aperture stop 15 on the one hand and the imaging scale ratioβ_(x)/β_(y) on the other hand.

The calculation explained above in connection with FIGS. 11 to 25 isalso carried out below for the further Δz defocusing displacements ofthe lithography mask 5, Δz_(LM), that are to be emulated. For thispurpose, the directional components are selected according to the curvesshown in FIG. 10 for the displacements Δz_(LM) of 50 nm, 0 nm, −50 nmand −100 nm. For intermediate Δz_(LM) displacements, corresponding 2Dimaging-light intensity distributions are selected, obtained by eitherbeing measured for corresponding Δz_(i) values or by being interpolated.

The method described above in connection with FIGS. 11 to 25 wasdescribed with an overly coarse determination of the result image, withjust four different defocusing values and assigned selection functions.By using a greater number of defocusing values, for example by usingmore than five defocusing values, more than ten defocusing values, byusing thirteen or seventeen defocusing values, by using more than twentydefocusing values, for example by using twenty-five defocusing values,and at the same time using a corresponding number of selection functionswith fine angle sector selection, an accuracy of the determination ofthe result image can be correspondingly improved further.

As an alternative to a digital selection function, which can only assumethe values 0 and 1, as explained above in conjunction with the selectionfunctions shown in FIGS. 19 to 22, a selection function with acontinuous transition between the values 0 and 1 may also be used. Thesealternative selection functions with a continuous transition are alsochosen such that they satisfy a normalizing condition, therefore thatthey ultimately select each point of the xy area with a weighting of 1.

The reconstruction method was described above with a configuration inwhich a distortion step with the imaging scale ratio of the lithographicprojection optical unit 21 represents the last method step. It isalternatively possible to distort the 2D imaging-light intensitydistributions first measured in measuring step 28 with the imaging scaleratio of the lithographic projection optical unit 21 and then carry outthe other reconstruction steps for measuring the 3D aerial image, inparticular the Fourier transformation, the selection of the directionalcomponents, the addition of the directional components and the inverseFourier transformation.

What is claimed is:
 1. A method for three-dimensionally measuring a 3Daerial image in the region around an image plane during the imaging of alithography mask, which is arranged in an object plane, while takinginto account a selectable imaging scale ratio in mutually perpendiculardirections with the following steps: performing a manipulation of apupil of an imaging optical unit used for the imagining of thelithography mask, inclusion of an influencing variable in the imaging ofthe lithography mask, in which the influencing variable corresponds tothe imaging scale ratio, performing a digital simulation step usinginformation from the pupil manipulation step and from the inclusion stepto generate a 3D aerial image, and output of the 3D aerial imagemeasured with the inclusion of the influencing variable.
 2. The methodaccording the claim 1, wherein the measurement is carried out with ameasuring optical unit, the imaging scale of which is the same inmutually perpendicular directions, the inclusion of the influencingvariable being performed by converting the data of a measured 2Dimaging-light intensity distribution in the region of a planecorresponding to the image plane.
 3. The method according to claim 1,wherein the inclusion of the influencing variable corresponding to theimaging scale ratio is performed by a digital simulation of the imagingwith the imaging scale ratio.
 4. A metrology system forthree-dimensionally measuring a 3D aerial image in the region around animage plane during the imaging of a lithography mask, which is arrangedin an object plane, in which the metrology system is configured to takeinto account a selectable imaging scale ratio in mutually perpendiculardirections with the following steps: performing a manipulation of apupil of an imaging optical unit used for the imagining of thelithography mask, inclusion of an influencing variable in the imaging ofthe lithography mask, in which the influencing variable corresponds tothe imaging scale ratio, performing a digital simulation step usinginformation from the pupil manipulation step and from the inclusion stepto generate a 3D aerial image, and output of the 3D aerial imagemeasured with the inclusion of the influencing variable; wherein themetrology system comprises: an illumination optical unit forilluminating the lithography mask to be examined, and an imaging opticalunit for imaging the object towards a spatially resolving detectiondevice.
 5. The metrology system of claim 4, in which the metrologysystem is configured to carry out the following steps to prepare theoutput of the 3D aerial image: measuring a 2D imaging-light intensitydistribution in the region of a plane corresponding to the image plane,displacing the lithography mask perpendicularly to the object plane by apredetermined displacement, and repeating the “measuring” and“displacing” steps until a sufficient number of 2D imaging-lightintensity distributions to reproduce a 3D aerial image are measured. 6.The metrology system of claim 5, comprising a measuring optical unitconfigured to carry out the measurement, the imaging scale of which isthe same in mutually perpendicular directions, the inclusion of theinfluencing variable being performed by converting the data of themeasured 2D imaging-light intensity distribution.